Hypothesis Testing for Difference Between Two Groups (i.e. Independence).

The idea is that you want to test whether or not a categorical variable (group variable) affects a numerical variable. Example: Does lemur taxonomy affect lifespan?

We want to test if mongoose lemurs have a greater median lifespan than the red-bellied lemurs.

Construct a hypothesis test to investigate the difference in median age of death between the two groups using age_at_death_y.

1. State the null and alternative hypothesis mathematically and in words.

2. Compute the sample statistic (what is the observed difference between the two groups?). Save this quantity as diff_med. Check the codebook to decode taxon names. You can remove NA observations.

3. Filter your data frame to contain only the two taxa of lemurs you care about. Save this new data frame as lemurs2. Simulate under the null using the template code below.

• Hint: reponse is the dependent variable while explanatory is the independent variable. Think about the prompt above: “does lemur taxonomy affect lifespan?”
• Once you complete the code chunk, remove eval = FALSE.

set.seed(63)

null_diff_life <- lemurs2 %>%
   specify(response = ___, explanatory = ___) %>%
   hypothesize(null = ___) %>%
   generate(reps = 500, type = ___) %>% # change reps to 15000 for final version
   calculate(stat = ___, order = c("EMON", "ERUB")) # specifies order

4. Compute the p-value using the get_pvalue() function. In narrative, use inline code to compare the p-value with \(\alpha = 0.05\) and make a conclusion. Be sure to state your conclusion in context.

Hypothesis Testing About a Proportion

According to Duke’s lemur center 75% of breeding occurs during October and November. Since gestation lasts about 4.5 months, one might expect 75% of births to occur in March and April.

Do you believe the proportion of births in these two months is significantly different from the expectation?

5. As above, setup a hypothesis test to investigate, following each step below.

• Step 1: State the null and alternative hypothesis.

• Step 2: Compute the observed statistic. Hint: first mutate a new variable birth_3or4 to be TRUE if birth month is 3 or 4 and FALSE otherwise. Save your mutated variable in lemurs3.

• Step 3: Simulate the null distribution, specify the response to be the mutated variable you created above and success = "TRUE". Use the seed number 65.

• Step 4: Compute p-value and compare to \(\alpha = 0.05\). Write your conclusion in context.

Hypothesis Testing and Confidence Interval About a Point Estimate

According to the Smithsonian’s National Zoo, the average weight of adult male ring-tailed lemurs is about 3 kilograms, and females are usually smaller.

Is adult, female, ring-tailed lemur weight significantly less than 3kg (3000g)?

6. Setup a hypothesis test to investigate, following each step below.

• Step 1: State the null and alternative hypothesis.

• Step 2: Filter your data frame to contain only the information you care about. Save this new data frame as lemurs4. Compute the observed statistic.

• Step 3: Simulate the null distribution using the seed number 66.

• Step 4: Visualize the null distribution with a p-value region shaded. Choose an informative label on the \(x\)-axis (e.g., sample proportion, sample median, etc.). Hint: use visualize() and shade_pvalue(). Compute p-value and compare to \(\alpha = 0.05\). Write your conclusion.

7. Construct a confidence interval with the confidence level equivalent to \(\alpha = 0.05\). Interpret the confidence interval. Use the same seed number as Ex 6. Is the conclusion drawn from the confidence interval consistent with the conclusion from the hypothesis test in Ex 6?